1 . 将函数
的零点按照从小到大的顺序排列,得到数列
,其前
项和为
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9c3cc4ba626cc12074542728cdfb930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352d9b76dcf639368fa68cae70149802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
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23-24高二下·全国·课前预习
2 . 等差数列的前
项和公式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
已知量 | 首项、末项与项数 | 首项、公差与项数 |
求和公式 | ![]() | ![]() |
您最近一年使用:0次
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3 . 记
表示k个元素的有限集,
表示非空数集E中所有元素的和,若集合
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33af7985fac2b7c4865d2f799baad783.png)
_____ ,若
,则m的最小值为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8fcb5a22de0e05657a3af45a0739e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed7239671dbc4429371f31db3b1efc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a8f8aae48c1483815eff5a6e3fb7b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33af7985fac2b7c4865d2f799baad783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817fc14a3ac8462a34b4b2f3bf07f13d.png)
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2024-05-04更新
|
431次组卷
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2卷引用:福建省三明市2024届普通高中高三毕业班质量检测数学试题
23-24高二下·全国·课前预习
解题方法
4 . 等差数列前
项和的性质
(1)若数列
是公差为
的等差数列,则数列
也是等差数列,且公差为______ .
(2)若
分别为等差数列
的前
项,前
项,前
项的和,则
,
也成等差数列,公差为______ .
(3)设两个等差数列
的前
项和分别为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6322378e9dc138599481f035cfe3b38.png)
______ .
(4)在等差数列中,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2e0d4d2e550f00b36d6f00111418ba.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dea1dd4ffcb4cf0697ca43079f6a1f2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35ddff98f658432f3723f43951abd46e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad491e5b5e14c49ef8b7004ebcfcef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade9841a8e6840efddcfd8620a6fc1fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b477afc102fe376cc777fffe0548cb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aacaf4a1b543085ebf2617cd600c011a.png)
(3)设两个等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/478421b81927e435cbcf5acafa89efd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6322378e9dc138599481f035cfe3b38.png)
(4)在等差数列中,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bcbc6ca5f2b222970ce2473603d54b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2e0d4d2e550f00b36d6f00111418ba.png)
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5 . 已知
是等差数列
的前
项和,若
,则数列
的前2024项和为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a517263344cbf74008f69565ee30c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8050391385b496e9c059201e4f12600a.png)
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6 . 参考《九章算术》中“竹九节”问题,提出:一根9节的竹子,自上而下各节的容积成等差数列,最上面3节的容积共3升,最下面3节的容积共6升,则第5节的容积为__________ 升.
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7 . 记
为等差数列
的前
项和,公差
不为0,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e843f5c36547fe7e3225956667fb55e.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f5c2f55631fd1ab756267c0f72e6cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e843f5c36547fe7e3225956667fb55e.png)
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2024-01-25更新
|
612次组卷
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4卷引用:四川省凉山州2023-2024学年高二上学期期末检测数学试卷
四川省凉山州2023-2024学年高二上学期期末检测数学试卷河北省衡水市冀州中学2024届高三第一次调研数学试题四川省广元市川师大万达中学2023-2024学年高二下学期入学考试数学试题(已下线)第五章:数列(单元测试)-2023-2024学年高二数学同步精品课堂(人教B版2019选择性必修第三册)
名校
解题方法
8 . 已知
为等差数列
的前n项和,
为其公差,且
,给出以下命题:
①
;②
;③使得
取得最大值时的n为8;④满足
成立的最大n值为17
其中正确命题的序号为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b2c87f9f5cf3c2e13c4e761eb5d36b4.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d8bbb4a09e0ac86bbae46222a90841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5084a907d0a5aab9003b5b342ce14c2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49763402b2f2023f0ba64c37924267d3.png)
其中正确命题的序号为
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解题方法
9 . 等差数列
的前
项和为
,
,则
=__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d016134e868cdad2396a514966c29d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27182444d3da4003680f07ec299087c.png)
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2024-01-23更新
|
656次组卷
|
3卷引用:内蒙古自治区赤峰市红山区2023-2024学年高二上学期期末学情监测数学试卷(B)
内蒙古自治区赤峰市红山区2023-2024学年高二上学期期末学情监测数学试卷(B)(已下线)5.2.2等差数列的前n项和(分层练习,7大题型)-2023-2024学年高二数学同步精品课堂(人教B版2019选择性必修第三册)河北省部分示范性高中2024届高三下学期一模数学试题
10 . 设
为等差数列
的前
项和,且
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd228d062d4085e949535cc73bae014.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8657a9f3eec0c1b0efa818f778129e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdba8a48eec7c0b90e22fa478d8f0ca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd228d062d4085e949535cc73bae014.png)
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